Another common approach to quantify the error of digital quantum simulation is to take the maximum expectation \(\max _{{\psi _\eta }}\left|{\psi _\eta }\cdot {\psi _\eta }\right|\)  within the \(\eta \) -electron manifold. This approach is used by previous work [1]}, [2]}, [3]} and appears to give a natural metric when digital quantum simulation is used as a subroutine in phase estimation. We show that this only differs from our definition (REF ) by at most a constant factor, reaffirming the fermionic seminorm as a proper error metric for simulating fermionic systems.
